Answering in reverse:
Question 2. First, the examples in the cited paper on power estimates are for large numbers of clusters, each of relatively small size. The plots of minimum detectable effect sizes (MDES) (Figures 1,2,3) only go up to 30 individuals per cluster and 150 clusters: at most 4500 individuals. You have a different situation: 17 clusters with at least 710 individuals each, over 12,000 individuals. That's more cases than any scenario I saw in a brief look at the paper. The total number of cases typically matters most.
Second, your model seems much less complex than the one illustrated in that paper. The model in the paper allows for a large number of potentially correlated random effects. For example, consider what would happen if your model included random effects for both your fixed-effect terms and for their interaction. The last model in the Mike Lawrence answer on the lmer
cheat sheet is for such a model: it requires 14 coefficient estimates. In your case, the constant value of pred2
within each L2 level allows you to omit that as a random effect among clusters
. You also omitted the pred1:pred2
interaction as a random effect,* further simplifying the model from what it might have been. I think your model only needs to estimate 6 coefficients.
Third, with only 17 clusters you will nevertheless have imprecise estimates of the variance and covariance of the random intercepts and slopes among clusters.
Question 1. Some recommendations to do "post-hoc power analysis" might not be so useless as they seem at first glance. An a priori power estimate to design a study for mixed-model analysis necessarily makes a lot of assumptions, as the linked paper explains. Re-examining those assumptions based on the observed data can provide both resolution of prior misconceptions and guidance for designing future studies. One might quibble over the terminology of "post-hoc power analysis." Whatever you call it, however, it's a good idea to evaluate what went right and what went wrong after you complete a study. For complicated mixed models, there is probably no better choice for that than simulations, as performed for example with the simr
package used in the paper.
*I'm not sure about the wisdom of this omission, but I confess to having a lot of problems thinking about mixed models with interactions.
Best Answer
I'm not sure you need simulation for a simple regression model. For example, see the paper Portable Power, by Robert E. Wheeler (Technometrics , May, 1974, Vol. 16, No. 2). For more complex models, specifically mixed effects, the pamm package in R performs power analyses through simulations. Also see Todd Jobe's post which has R code for simulation.